Tight-binding $\varepsilon_k=-2t\cos k $, bandwidth $ W=4t $. Self-energy $ \Sigma(\omega)=\frac{U^2}{4}\,\frac{1}{\omega+i\eta} $.
Adds a frequency-dependent ImΣ on top of the constant η.
Show DOS $ \rho(\omega) $
Show $ A(k,\omega) $ heatmap
Overlay non-interacting band